Polarization modulation ranging signal denoising method based on EMD (Empirical Mode Decomposition) and dynamic median filtering

Abstract

The invention provides a polarization modulation ranging signal denoising method based on EMD (empirical mode decomposition) and dynamic median filtering, which comprises the following steps: acquiring an original polarization modulation ranging signal, converting the original polarization modulation ranging signal into a one-dimensional column vector format, and performing polynomial fitting continuation on two ends of the obtained one-dimensional column vector signal; decomposing the extended signal by adopting an empirical mode decomposition algorithm to obtain a plurality of IMFs and a residual error; calculating the standard deviation and energy of each IMF in the plurality of IMFs and the total energy of the plurality of IMFs; dividing the plurality of IMFs into useful IMF components and noise IMF components based on a preset energy proportion threshold value and the proportion of the energy of each IMF in the total energy; for the noise IMF component, a median filtering window is dynamically generated according to the standard deviation of the noise IMF component, and median filtering is executed; superposing the filtered noise IMF component, the useful IMF component and the residual error to obtain a denoised reconstructed signal; and calculating a signal-to-noise ratio and a root-mean-square error of the denoised reconstructed signal, and evaluating a denoising effect. According to the invention, rapid, efficient and accurate noise reduction is realized.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for denoising polarization modulation ranging signals based on EMD and dynamic median filtering. Background Technology

[0002] Laser absolute distance measurement technology, with its non-contact and fast response characteristics, has been widely used in many fields such as industrial manufacturing, precision instrument calibration, and aerospace, becoming one of the indispensable core methods in modern measurement technology. However, laser absolute distance measurement technology still has common limitations in practical applications: on the one hand, it is difficult to meet the high-precision measurement requirements in precision scenarios; on the other hand, it has shortcomings in environmental adaptability, generally requiring high stability of the measurement light and having weak anti-interference ability, making it difficult to adapt to complex industrial sites.

[0003] The emergence of polarization modulation ranging technology has provided a new research direction for high-precision ranging. Polarization modulation ranging technology transforms the phase detection problem into a frequency measurement problem, and calculates the distance to be measured by sweeping the frequency, avoiding distance ambiguity. It does not require complex structures and has strong anti-interference capabilities. However, it has low resolution at minimum light intensity and is susceptible to noise interference, leading to fitting difficulties and thus affecting the ranging results.

[0004] Existing denoising techniques, such as Chinese patent CN115700544A, combine empirical mode decomposition (EMD) and wavelet soft thresholding to denoise chromatographic signals. However, they only use the first 1 / 3 of the high frequencies as the noise selection rule, and the wavelet filter parameters are fixed, making it impossible to dynamically match the signal characteristics of different layers. Chinese patent CN114098656A uses EMD as a basis and combines bit-plane transformation to achieve signal denoising. During reconstruction, the selection of IMF components is determined manually, and different selections may lead to different results. At the same time, the residual obtained from decomposition is not included, which may result in the loss of low-frequency trends. Chinese patent CN115211869B uses EMD and Kalman filtering for combined denoising, but it does not solve the endpoint effect that exists in EMD.

[0005] In summary, existing noise reduction technologies mainly suffer from the following drawbacks: (1) When EMD decomposes polarization modulation ranging signals, there is an endpoint effect, which causes the IMF components at both ends of the signal to be distorted.

[0006] (2) The existing filtering parameters are fixed and cannot be adapted to different IMF component noise characteristics, making it difficult to balance the denoising effect and signal fidelity.

[0007] (3) Existing technologies tend to lose low-frequency trends when reconstructing signals.

[0008] (4) Existing technologies cannot solve the problem of background noise interference in polarization modulation ranging signals, resulting in insufficient noise reduction efficiency and accuracy. Summary of the Invention

[0009] This invention provides a method for denoising polarization modulation ranging signals based on EMD and dynamic median filtering, in order to at least solve the above-mentioned technical problems.

[0010] According to a first aspect of the present invention, an EMD-based... A method for denoising polarization modulation ranging signals using dynamic median filtering includes: acquiring the original polarization modulation ranging signal and converting it into a one-dimensional column vector format to obtain a one-dimensional column vector signal; performing polynomial fitting and extension on both ends of the one-dimensional column vector signal to obtain an extended signal; decomposing the extended signal using an empirical mode decomposition algorithm to obtain multiple IMFs and a residual; calculating the standard deviation of each IMF, the energy of each IMF, and the total energy of the multiple IMFs; dividing the multiple IMFs into useful IMF components and noise IMF components based on a preset energy proportion threshold and the proportion of the energy of each IMF in the total energy of the multiple IMFs; dynamically generating a median filtering window based on the standard deviation of the noise IMF component, and performing median filtering on the noise IMF component according to the median filtering window to obtain a filtered noise IMF component; superimposing the filtered noise IMF component, the useful IMF component, and the residual to obtain a denoised reconstructed signal; and evaluating the denoising effect by calculating the signal-to-noise ratio and root mean square error of the denoised reconstructed signal.

[0011] According to a second aspect of the present invention, a polarization modulation ranging signal denoising device based on EMD and dynamic median filtering is provided, comprising: a raw signal acquisition and preprocessing module for acquiring the raw polarization modulation ranging signal and converting it into a one-dimensional column vector format to obtain a one-dimensional column vector signal; a polynomial extension module for performing polynomial fitting extension on both ends of the one-dimensional column vector signal to obtain an extended signal; and an EMD decomposition module for decomposing the extended signal using an empirical mode decomposition algorithm to obtain multiple IMFs and a residual; the IMFs are... The system includes a sorting and feature calculation module for calculating the standard deviation of each IMF, the energy of each IMF, and the total energy of the multiple IMFs; an IMF classification module for classifying the multiple IMFs into useful IMF components and noise IMF components based on a preset energy proportion threshold and the proportion of each IMF's energy in the total energy of the multiple IMFs; a dynamic median filtering module for dynamically generating a median filtering window for the noise IMF components based on their standard deviation, and performing median filtering on the noise IMF components according to the median filtering window to obtain filtered noise IMF components; and a signal reconstruction and effect verification module for superimposing the filtered noise IMF components, the useful IMF components, and the residuals to obtain a denoised reconstructed signal, and evaluating the denoising effect by calculating the signal-to-noise ratio and root mean square error of the denoised reconstructed signal.

[0012] Compared with existing technologies, this invention first extends the original polarization modulation ranging signal through polynomial fitting to specifically address the endpoint effect of EMD decomposition; then, it adaptively decomposes the signal into multiple intrinsic mode functions (IMFs) and residuals using EMD; subsequently, it quickly distinguishes between "useful IMFs" and "noise IMFs" based on energy proportions. Compared with traditional methods that directly remove noise IMFs, this invention designs a dynamic filtering window based on the standard deviation characteristics of noise IMFs, accurately filtering each component; the reconstructed signal retains the residuals obtained from the decomposition and preserves the low-frequency trend, thus thoroughly eliminating noise interference while preserving key signal details and low-frequency trends to the greatest extent, solving the core pain points of existing technologies and achieving fast, efficient, and accurate noise reduction processing. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0014] Figure 1 This is a flowchart of the steps of the method of the present invention.

[0015] Figure 2 To and Figure 1 The overall flowchart of the method of the present invention is shown below.

[0016] Figure 3 This is a schematic diagram of a polarization modulation ranging system according to the present invention.

[0017] Figure 4 This is a schematic diagram of the initial signal of the present invention.

[0018] Figure 5 This is a schematic diagram of EMD decomposition and noise determination according to the present invention.

[0019] Figure 6 This is a schematic diagram of the noise signal and the filtered signal of the present invention.

[0020] Figure 7 This is a schematic diagram comparing the original signal and the reconstructed signal of the present invention. Detailed Implementation

[0021] To provide a clearer understanding of the technical features, objectives, and effects of the embodiments of the present invention, specific implementation methods of the embodiments of the present invention will now be described with reference to the accompanying drawings.

[0022] In this document, “exemplary” means “serving as an example, illustration or description”, and any illustrations or implementations described herein as “exemplary” should not be construed as a more preferred or advantageous technical solution.

[0023] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0024] The specific implementation of the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0025] See Figure 1 The present invention provides a method for denoising polarization modulation ranging signals based on EMD and dynamic median filtering, which specifically includes the following steps: Step S101: Obtain the original polarization modulation ranging signal and convert it into a one-dimensional column vector format to obtain a one-dimensional column vector signal; Step S102: Perform polynomial fitting and extension on both ends of the one-dimensional column vector signal to obtain the extended signal; Step S103: Decompose the extended signal using the empirical mode decomposition algorithm to obtain multiple IMFs and a residual; Step S104: Calculate the standard deviation of each IMF, the energy of each IMF, and the total energy of the multiple IMFs; Step S105: Based on a preset energy percentage threshold and the percentage of energy of each IMF in the total energy of the multiple IMFs, the multiple IMFs are divided into useful IMF components and noise IMF components; Step S106: For the noise IMF component, a median filtering window is dynamically generated based on its standard deviation, and median filtering is performed on the noise IMF component based on the median filtering window to obtain the filtered noise IMF component. Step S107: The filtered noise IMF component, the useful IMF component, and the residual are superimposed to obtain the denoised reconstructed signal; Step S108: Evaluate the denoising effect by calculating the signal-to-noise ratio and root mean square error of the reconstructed signal after denoising.

[0026] Optionally, the step of performing polynomial fitting and extension on both ends of the one-dimensional column vector signal to obtain the extended signal includes: presetting the order of the polynomial according to the length of the one-dimensional column vector signal; performing polynomial fitting on the edge data at both ends of the one-dimensional column vector signal based on the preset polynomial order to generate extended data; and concatenating the extended data to the beginning and end of the one-dimensional column vector signal to obtain the extended signal.

[0027] Optionally, the standard deviation is expressed as:

[0028] in, Let be the mean of the i-th IMF, i.e.:

[0029] in, This represents the j-th sampling point of the i-th IMF.

[0030] Optionally, the energy is represented as:

[0031] The total energy of the multiple IMFs is expressed as: .

[0032] Optionally, the step of dividing the multiple IMFs into useful IMF components and noisy IMF components based on a preset energy proportion threshold and the proportion of each IMF's energy in the total energy of the multiple IMFs includes: the preset energy proportion threshold is... For the i-th IMF, calculate the proportion of its energy to the total energy of the multiple IMFs:

[0033] like If the i-th IMF is determined to be a noise IMF component; Otherwise, the i-th IMF is determined to be a useful IMF component.

[0034] Optionally, the step of dynamically generating a median filtering window based on the standard deviation of the noise IMF component, and performing median filtering on the noise IMF component according to the median filtering window to obtain the filtered noise IMF component, includes: For the i-th noise IMF component, a fixed coefficient k is set, and its initial window is calculated:

[0035] To meet the median filtering requirements, the initial window size is odd, where, Display window Remainder when divided by 2:

[0036] Set window thresholds, including: setting the minimum window min_win and setting the maximum window max_win; Determine if the window size meets the set window threshold requirement:

[0037] Use the final window The median filtering window is used to perform median filtering on the i-th noise IMF component to obtain the filtered i-th noise IMF component.

[0038] Optionally, the denoised reconstructed signal is represented as: .

[0039] Optionally, the signal-to-noise ratio is used to reflect the degree of noise reduction, and the calculation formula is as follows:

[0040] in, .

[0041] Optionally, the root mean square error is used to reflect the degree of agreement between the denoised reconstructed signal and the original polarization modulation ranging signal, and is calculated using the following formula: .

[0042] This invention proposes a polarization modulation ranging signal denoising method based on EMD and dynamic median filtering. It suppresses the endpoint effect of EMD decomposition by polynomial extension of both ends of the signal; it divides the useful and noisy signals according to the IMF energy ratio; for the noisy signal, it dynamically adjusts the median filtering window size based on its IMF standard deviation; during reconstruction, it fuses the useful IMF component, and the filtered IMF component and residual retain the low-frequency trend, achieving fast, efficient, and accurate denoising processing.

[0043] Specifically, the solution of the present invention is further described with reference to the following examples: See Figure 2 This embodiment mainly includes the following steps: S1. Obtain the original polarization modulation ranging signal data, convert it into column vector format to obtain a one-dimensional column vector signal, and calculate the data length L.

[0044] S2. Perform polynomial fitting and extension on both ends of the one-dimensional column vector signal to obtain the extended signal. The extension length is 10% of the signal length.

[0045] S3. The extended signal is decomposed using the Empirical Mode Decomposition (EMD) algorithm to obtain N Intrinsic Mode Functions (IMFs) and 1 Residue (res); the IMF components are naturally ordered in the order of "high frequency → low frequency", and the residual is the low-frequency trend skeleton of the signal.

[0046] S4. For the i-th IMF component obtained from the decomposition (denoted as IMF_i), which contains N sampling points, i.e., IMF_i = [imf_{i,1}, imf_{i,2}, ..., imf_{i,N}], where imf_{i,j} represents the j-th sampling point of the i-th IMF (j=1,2,...,N), calculate the following two quantization metrics: (1) Standard Deviation (STD) reflects the volatility of the i-th IMF, and is calculated using the following formula:

[0047] in, Let be the mean of the i-th IMF, i.e.:

[0048] (2) Energy (E), which reflects the energy of the i-th IMF, is calculated using the following formula:

[0049] Simultaneously, calculate the total energy (TE) of the N IMFs:

[0050] S5, Preset energy percentage threshold For the i-th IMF, calculate its energy as a percentage of the total energy (Ratio, R):

[0051] like If the i-th IMF is positive, then the i-th IMF is determined to be a noise IMF component; otherwise, it is determined to be a useful IMF component.

[0052] S6. For IMFs identified as noise components, a median filter window is dynamically generated based on their standard deviation. The specific process is as follows: S6.1 Set a fixed coefficient k and calculate the initial window:

[0053] S6.2 To meet the median filtering requirements, the initial window size is made odd, where, Display window Remainder when divided by 2:

[0054] S6.3 Set window thresholds, i.e., minimum window min_win to avoid insufficient noise processing; maximum window max_win to avoid over-processing, which could lead to signal distortion.

[0055] S6.4 Determine if the window size meets the threshold requirement:

[0056] S6.5, Use the final window Median filtering is applied to the i-th IMF.

[0057] S7. Repeat steps S5-S6 for the i-th (i = 1, 2, ..., N) IMF in sequence to complete the "type determination - noise filtering" process for all IMFs.

[0058] S8. The processed noise component (i.e., the filtered noise IMF component), the unprocessed useful component (i.e., the useful IMF component), and the residual are superimposed to obtain the denoised reconstructed signal:

[0059] S9. Calculate the signal-to-noise ratio (SNR) and root mean square error (RMSE) to verify the denoising effect. The signal-to-noise ratio (SNR) reflects the degree of noise reduction, and the formula is as follows:

[0060] in, .

[0061] The root mean square error (RMSE) reflects the degree of agreement between the denoised reconstructed signal and the original signal, i.e., the original polarization-modulated ranging signal. The formula is: .

[0062] The method of the present invention is applied to, for example Figure 3 The polarization modulation ranging system shown includes the following components: laser source, collimator, grating isolator, modulator, quarter-wave plate, reflective target sphere, photodetector, data acquisition card, radio frequency signal source, and computer.

[0063] The laser emits a laser beam, which is coupled into the input of a collimator via a single-mode fiber. The collimated laser output from the collimator enters an isolator, which only allows unidirectional laser light to pass through to prevent backlighting. The laser emitted from the isolator enters a polarization beam splitter and then enters an optoelectronic phase modulator for modulation. The laser modulated by the optoelectronic phase modulator passes through a quarter-wave plate, is reflected by the target sphere, and then passes back through the quarter-wave plate to enter the optoelectronic phase modulator for secondary modulation. The secondary modulated laser is polarized at the polarization beam splitter, converted into an electrical signal by a detector, acquired by a data acquisition card, and uploaded to a PC for storage. A continuously sweeping frequency signal is applied to the photoelectric phase modulator, and the light intensity signal measured by the photodetector is as follows:

[0064] Among them, I F M is the light intensity, and M is the electro-optic modulation depth. The phase difference of the modulated signal caused by the time of flight, L d Where c is the distance to be measured, and c is the speed of light. It is the sweep frequency. When the phase difference yes When the frequency is an integer multiple, the probe light intensity is at its minimum, and the distance to be measured is related to the sweep frequency. The relationship is:

[0065] Because the periodicity of the sinusoidal function leads to multiple solutions for the distance to be measured, it is necessary to obtain light intensity signals at multiple modulation frequencies through continuous frequency sweeping to obtain a single solution for the distance. The frequencies corresponding to two consecutive minimum light intensity values ​​are measured, i.e., the first frequency. Second frequency The relationship between the frequency of adjacent minimum light intensity points and the distance to be measured is as follows:

[0066] After solving the two equations simultaneously to find N, the distance to be measured can be calculated:

[0067] A frequency sweep signal of 2200-2300MHz with 1MHz steps is applied to the polarization modulation system to obtain the approximate location of the minimum point; then, a local fine frequency sweep is performed within the range to the left and right of the minimum point, as shown in the figure. Figure 4 As shown.

[0068] As described in the steps above, set the energy percentage threshold. , , The frequency sweep data (raw signal) is processed, and the decomposition results, noise determination, and window size are as follows: Figure 5 As shown, the comparison of the noise signal before and after IMF filtering is as follows: Figure 6 As shown.

[0069] Reconstructed signal such as Figure 7 As shown, the reconstructed signal SNR is 39.46 dB and RMSE is 0.0032, indicating that noise suppression and signal fidelity are effectively achieved, verifying the reliability of the method proposed in this invention.

[0070] This invention first extends the original polarization-modulated ranging signal through polynomial fitting to specifically address the endpoint effect of EMD decomposition. Then, it adaptively decomposes the signal into multiple intrinsic mode functions (IMFs) and residuals using EMD. Subsequently, it quickly distinguishes between "useful IMFs" and "noise IMFs" based on energy proportions. Compared to traditional methods that directly remove noise IMFs, this invention designs a dynamic filtering window based on the standard deviation characteristics of noise IMFs, accurately filtering each component. The reconstructed signal retains the residuals obtained from the decomposition and preserves low-frequency trends. Compared to traditional fixed-window filtering, this scheme thoroughly eliminates noise interference while preserving key signal details and low-frequency trends to the greatest extent, solving the core pain points of existing technologies. The specific beneficial effects of this invention include: (1) By dividing useful signals into noise signals by energy, it is simple, fast and targeted: useful signals usually contain high energy, while noise is mostly low-energy random components. This invention does not require complex time-frequency analysis or prior knowledge, and can quickly distinguish useful components from noise components to be processed, reducing the probability of useful signals being misjudged as noise and improving the accuracy of separation.

[0071] (2) Adaptive filtering window design to balance denoising effect and fidelity: Median filtering has a natural advantage over impulse noise and spike interference, but traditional fixed-window median filtering has limitations: if the window is too small, it will not be able to effectively filter out strong noise, and if the window is too large, it will smooth out useful details. However, this invention sets different windows according to the standard deviation of the noise IMF, so that the filtering intensity matches the noise fluctuation: a larger window is used for noise IMF with a large standard deviation (violent fluctuation and stronger noise) to enhance the denoising effect; a smaller window is used for noise IMF with a small standard deviation (smooth fluctuation and may contain weak useful components) to reduce excessive smoothing of details. The adaptive window design retains the useful information that may be hidden in the noise IMF to the greatest extent while denoising.

[0072] (3) Full component reconstruction reduces the loss of effective information: In the reconstruction process, the present invention directly retains useful IMF, optimizes noise IMF filtering, and completely retains residuals, avoiding the loss of signal details or trends caused by "directly removing noise IMFs"; the retention of residuals can maintain the overall trend of the signal, while the filtered noise IMFs remove interference.

[0073] In summary, this invention, through a closed-loop design of "polynomial extension to solve end-point effects → precise energy proportion division of IMF → dynamic window adaptive filtering → full component reconstruction," leverages the decomposition advantages of EMD while overcoming the adaptability and fidelity deficiencies of traditional denoising techniques. This method rapidly and efficiently removes noise while fully preserving key signal details and low-frequency trends, improving the signal-to-noise ratio and waveform integrity of polarization-modulated ranging signals, and providing core technical support for subsequent improvements in ranging accuracy.

[0074] As another example, the present invention also provides a polarization modulation ranging signal denoising device based on EMD and dynamic median filtering, comprising: The original signal acquisition and preprocessing module is used to acquire the original polarization modulation ranging signal and convert it into a one-dimensional column vector format to obtain a one-dimensional column vector signal. The polynomial extension module is used to perform polynomial fitting and extension on both ends of the one-dimensional column vector signal to obtain the extended signal. The EMD decomposition module is used to decompose the extended signal using the empirical mode decomposition algorithm to obtain multiple IMFs and a residual. The IMF ranking and feature calculation module is used to calculate the standard deviation of each IMF, the energy of each IMF, and the total energy of the multiple IMFs. The IMF classification module is used to classify the multiple IMFs into useful IMF components and noise IMF components based on a preset energy percentage threshold and the percentage of the energy of each IMF in the total energy of the multiple IMFs. The dynamic median filtering module is used to dynamically generate a median filtering window based on the standard deviation of the noise IMF component, and perform median filtering on the noise IMF component based on the median filtering window to obtain the filtered noise IMF component. The signal reconstruction and effect verification module is used to superimpose the filtered noise IMF component, the useful IMF component and the residual to obtain the denoised reconstructed signal, and evaluate the denoising effect by calculating the signal-to-noise ratio and root mean square error of the denoised reconstructed signal.

[0075] For example, the solution of the present invention uses "signal acquisition-preprocessing-decomposition-classification-dynamic filtering-reconstruction verification" as the core logic to build a modular functional architecture, the specific structure of which is as follows: 1. Raw signal acquisition and preprocessing module Module composition: Includes signal acquisition unit, format conversion unit, and length calculation unit.

[0076] The signal acquisition unit is adapted to the polarization modulation ranging system hardware and is responsible for acquiring and storing the raw polarization modulation ranging signal.

[0077] The format conversion unit converts the acquired one-dimensional raw signal into a column vector format.

[0078] Length calculation unit: Simultaneously calculates the total length of the column vector signal, i.e., the one-dimensional column vector signal, providing basic parameters for subsequent extension and filtering window settings.

[0079] The signal format is standardized as a column vector, which facilitates subsequent algorithm operations (EMD decomposition, median filtering); the signal length is obtained in advance to provide data support for the adaptive adjustment of parameters in subsequent modules and avoid dimension mismatch problems during processing.

[0080] 2. Polynomial Extension Module Module composition: extension parameter configuration unit, polynomial fitting unit.

[0081] The extension parameter configuration unit presets the polynomial order (e.g., 3rd or 5th order) based on the length of the one-dimensional column vector signal.

[0082] The polynomial fitting unit performs polynomial fitting on the beginning and end edge data of the one-dimensional column vector signal based on a preset order, generates extended data, and splices it to both ends of the one-dimensional column vector signal to obtain the extended signal.

[0083] To address the "edge effect" problem in EMD decomposition—the original signal edge data lacks contextual support, and direct decomposition can easily lead to distortion of IMF components. Polynomial extension supplements the data by fitting edge trends, ensuring the integrity and accuracy of each IMF after decomposition.

[0084] 3. EMD Decomposition Module Module composition: EMD algorithm execution unit.

[0085] The EMD algorithm execution unit decomposes the extended signal to obtain multiple intrinsic mode functions (IMFs) and one residual.

[0086] 4. IMF Ranking and Feature Calculation Module Module composition: frequency sorting unit and feature parameter calculation unit.

[0087] The frequency sorting unit extracts the instantaneous frequency of each IMF and sorts all IMFs in the order of "high frequency → low frequency".

[0088] The characteristic parameter calculation unit calculates the standard deviation (reflecting the degree of signal fluctuation), energy (reflecting the signal strength), and total energy of all IMFs for each IMF, and then derives the energy ratio of each IMF (energy of a single IMF / total energy).

[0089] 5. IMF Classification Module Module composition: threshold unit, classification judgment unit.

[0090] Threshold unit: Customize the energy percentage threshold according to the ranging scenario (such as low noise environment, strong interference environment).

[0091] Classification and Judgment Unit: The energy percentage of each IMF is compared with a set threshold. If it is less than the threshold, it is judged as a noise IMF component; if it is greater than the threshold, it is judged as a useful IMF component.

[0092] Quantitative classification based on energy percentage is more objective and flexible than subjective judgment or fixed rule classification; it can also adapt to scenarios with different noise intensities by adjusting the threshold, thus improving the versatility of the solution.

[0093] 6. Dynamic Median Filtering Module Module composition: window initialization calculation unit, window odd number processing unit, window upper and lower limit constraint unit, and filtering execution unit.

[0094] Initial Window Calculation Unit: Based on the standard deviation of each noise IMF component, adaptively calculate the initial median filter window (the larger the standard deviation, the larger the initial window, to adapt to strong noise; the smaller the standard deviation, the smaller the initial window, to adapt to weak noise).

[0095] Odd-number window processing unit: Through the logic of "initial window - remainder + 1" (the remainder is the result of dividing the initial window by 2), it ensures that the window size is always odd, which satisfies the core requirement of median filtering (an odd-numbered window can uniquely determine the median position).

[0096] Window upper and lower limit constraint unit: preset minimum odd window and maximum odd window, and restrict the odd-numbered window - if it is less than the minimum value, use the minimum value; if it is greater than the maximum value, use the maximum value; if it is within the interval, use the calculated value.

[0097] Filtering execution unit: For each noise IMF, apply its corresponding constrained window and perform median filtering.

[0098] The dynamic window design solves the shortcomings of traditional fixed-window mid-range filtering—matching different windows to IMFs with different noise intensities, avoiding "insufficient denoising due to excessively small windows" or "signal distortion due to excessively large windows"; odd numbering and upper and lower limit constraints further ensure the stability and effectiveness of filtering, balancing denoising effect and signal fidelity.

[0099] 7. Signal Reconstruction and Effect Verification Module Module composition: overlay unit, performance index calculation unit.

[0100] The superposition unit superimposes the filtered noise IMF, the unfiltered useful IMF, and the residual to generate a reconstructed signal.

[0101] The performance index calculation unit calculates the signal-to-noise ratio (SNR) and root mean square error (RMSE) of the reconstructed signal to quantitatively evaluate the denoising effect.

[0102] The reconstructed signal retains all useful signals and trend terms, while only the noise IMF is processed. The SNR and RMSE are used for quantitative verification to provide an objective evaluation standard for the denoising effect, which facilitates subsequent parameter optimization.

[0103] The apparatus in this embodiment is used to implement the corresponding methods in the foregoing multiple method embodiments and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0104] Specific embodiments of the invention have now been described. Other embodiments are within the scope of the appended claims. In some cases, the actions described in the claims can be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing can be advantageous.

[0105] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the embodiments of the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the embodiments of the present invention. Therefore, all equivalent technical solutions also fall within the scope of the embodiments of the present invention, and the patent protection scope of the embodiments of the present invention should be defined by the claims.

Claims

1. A polarization modulation ranging signal denoising method based on EMD and dynamic median filtering, characterized in that, The method comprises the following steps: obtaining an original polarization modulation ranging signal and converting it into a one-dimensional column vector format to obtain a one-dimensional column vector signal; polynomial fitting extension is performed on both ends of the one-dimensional column vector signal to obtain an extended signal; the extended signal is decomposed by using an empirical mode decomposition algorithm to obtain a plurality of IMFs and a residual; the standard deviation of each IMF, the energy of each IMF and the total energy of the plurality of IMFs are calculated; based on a preset energy proportion threshold and the proportion of the energy of each IMF in the total energy of the plurality of IMFs, the plurality of IMFs are divided into useful IMF components and noise IMF components; for the noise IMF component, a median filtering window is dynamically generated according to the standard deviation, and median filtering is performed on the noise IMF component according to the median filtering window to obtain a filtered noise IMF component; the filtered noise IMF component, the useful IMF component and the residual are superimposed to obtain a denoised reconstructed signal; the denoising effect is evaluated by calculating the signal-to-noise ratio and the root mean square error of the denoised reconstructed signal.

2. The method of claim 1, wherein, The polynomial fitting extension performed on both ends of the one-dimensional column vector signal to obtain an extended signal comprises: the order of the polynomial is preset according to the length of the one-dimensional column vector signal; based on the preset polynomial order, polynomial fitting is performed on the edge data at the two ends of the one-dimensional column vector signal to generate extension data; the extension data is spliced to the head and tail of the one-dimensional column vector signal respectively to obtain the extended signal.

3. The method of claim 1, wherein, The standard deviation is represented as: wherein, is the mean value of the i-th IMF, i.e.: wherein, denotes the jth sample point of the ith IMF.

4. The method of claim 1, wherein, The energy is represented as: The total energy of the plurality of IMFs is represented as: 。 5. The method of claim 4, wherein, based on a preset energy proportion threshold and the proportion of the energy of each IMF in the total energy of the plurality of IMFs, the plurality of IMFs are divided into useful IMF components and noise IMF components, comprising: The preset energy proportion threshold is For the i-th IMF, the proportion of its energy to the total energy of the plurality of IMFs is calculated: If then the i-th IMF is determined to be a noise IMF component; otherwise, the i-th IMF is determined to be a useful IMF component.

6. The method of claim 1, wherein, For the noise IMF component, a median filtering window is dynamically generated according to the standard deviation, and median filtering is performed on the noise IMF component according to the median filtering window to obtain a filtered noise IMF component, comprising: for the i-th noise IMF component, a fixed coefficient k is set, and the initial window is calculated: To meet the median filtering requirement, the initial window is made odd, where, represents the window remainder of division by 2: the window threshold is set, including setting the minimum window min_win and setting the maximum window max_win; it is judged whether the window size meets the set window threshold requirement: Adopting final window As the median filtering window, the i-th noise IMF component is median filtered to obtain a filtered i-th noise IMF component.

7. The method of claim 1, wherein, The denoised reconstructed signal is represented as: 。 8. The method of claim 1, wherein, The signal-to-noise ratio is used to reflect the degree of noise reduction, and the calculation formula is: wherein .

9. The method of claim 8, wherein, The root mean square error is used to reflect the degree of coincidence between the denoised reconstructed signal and the original polarization modulation ranging signal, and the calculation formula is: 。 10. An EMD and dynamic median filter based denoising device for polarization modulated ranging signals, characterized in that, comprising: an original signal acquisition and preprocessing module for obtaining an original polarization modulation ranging signal and converting it into a one-dimensional column vector format to obtain a one-dimensional column vector signal; a polynomial extension module for performing polynomial fitting extension on both ends of the one-dimensional column vector signal to obtain an extended signal; An EMD decomposition module is configured to decompose the extended signal by using an empirical mode decomposition algorithm to obtain a plurality of IMFs and a residual; An IMF sorting and feature calculation module is configured to calculate a standard deviation of each IMF, an energy of each IMF, and a total energy of the plurality of IMFs; An IMF classification module is configured to classify the plurality of IMFs into useful IMF components and noise IMF components based on a preset energy proportion threshold and a proportion of the energy of each IMF in the total energy of the plurality of IMFs; A dynamic median filtering module is configured to, for the noise IMF components, dynamically generate a median filtering window according to the standard deviation thereof, and perform median filtering on the noise IMF components according to the median filtering window to obtain filtered noise IMF components; A signal reconstruction and effect inspection module is configured to superimpose the filtered noise IMF components, the useful IMF components, and the residual to obtain a denoised reconstructed signal, and evaluate the denoising effect by calculating a signal-to-noise ratio and a root mean square error of the denoised reconstructed signal.

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